A new mixed integer linear programming model for the multi level uncapacitated facility location problem

Location selection of city logistics centers under sustainability

“…Since the 1970s, the literature is replete with work on location theory. We name a few recent key works for completeness, for example, the hybrid multi-start heuristic (Resende and Werneck, 2006), second-order cone programming (Wagner et al, 2009), approximation algorithms (Huang and Li, 2008;Li, 2013), greedy heuristic and fix-and-optimize heuristic (Ghaderi and Jabalameli, 2013), Lagrangian relaxation heuristic (Nezhad et al, 2013), mixed integer linear programming model (Kratica et al, 2014), discrete variant of unconscious search (Ardjmand et al, 2014), multi-objective optimization model (Tang et al, 2013), and the weighted Dantzig-Wolfe decomposition and path-relinking combined method , which have been presented for solving an uncapacitated facility location problem. Also, some algorithms and methods have been proposed for solving the capacitated facility location problem to optimality such as the mixed integer programming formulation (Melkote and Daskin, 2001;Aros-Vera et al, 2013;Rosa et al, 2014), branch-and-price algorithm (Klose and Görtz, 2007), Lagrangian heuristic algorithm (Wu et al, 2006;Elhedhli and Merrick, 2012), kernel search heuristic (Guastaroba and Speranza, 2014), Lagrangian Heuristic and Ant Colony System (Chen and Ting, 2008), Lagrangian relaxation algorithm (Yun et al, 2014), a fix-and-optimize heuristic based on the evolutionary fire-fly algorithm (Rahmaniani and Ghaderi, 2013), hybrid Firefly-Genetic Algorithm (Rahmani and MirHassani, 2014), swarm intelligence based on sample average approximation (Aydin and Murat, 2013), modified Clarke and Wright savings heuristic algorithm , iterated tabu search heuristic (Ho, 2015), improved approximation algorithm (Aardal et al, 2015), two-stage robust models and algorithms , and the evolutionary multi-objective optimization approach (Rakas et al, 2004;Harris et al, 2014).…”

Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location

“…For comparison purposes, we have adapted three known MILP formulations for the MUFLP to our more general MUpLP. These are a path-based formulation (PBF) (Aardal et al 1999, Edwards 2001, an arc-based formulation (ABF) (Aardal et al 1996, Gabor andvan Ommeren 2010) and a flow-based formulation (FBF) (Kratica et al 2014). These formulations are provided in the Online Appendix A.…”

Peer Review #1 of "An integrated platform for intuitive mathematical programming modeling using LaTeX (v0.2)"

“…The corpus of models invented for linear optimization over the past decades and for a multitude of domains has been consistently increasing. It can be easily demonstrated with examples in Machine Learning, Operations Research and Management Science, Physics, Information Security, Environmental Modeling and Systems Biology among many others (Yang et al, 2016;Tanveer, 2015;Silva et al, 2016;Sitek and Wikarek, 2015;Liu and Papageorgiou, 2018;Triantafyllidis et al, 2018;Cohen et al, 2017;Romeijn et al, 2006;Mitsos et al, 2009;Melas et al, 2013;Kratica et al, 2014;Mouha et al, 2012). This paper is organized as follows: in section 2, we describe the current functionality supported by the platform at this prototype stage.…”